I don't think this math checks out unless you have many rolls, not just the one. You cannot really calculate the statistical sum of the profits with a single dye roll. Just like you cannot calculate the average mean with only a single number as that would make the number the average mean itself and calculating it has no point. That just seems a bit silly, to be honest.
There is no need to calculate EV here. Its a one time thing, so either you win or you lose. The chances of winning is around 17%.
I would take the bet with twice the amount as a regular dice game. That seems like a reasonable amount. But I would be wary of betting more, as the large winnings do not have any effect on the probability. Its still the same chance of winning as in a regular dice game.
This was already discussed earlier in this thread, i.e. >
here<
EV is a wider concept than just calculating long-run winnings. Quick explanation:
- you would take a one-time coin-flip bet when for $1 wager you could win $100
- you wouldn't take such bet if for $1 wager you could only win $0.10
Why? You'd assess its EV, probably without realising it. All the relevant factors that you need to make a decision are the same as those used in the EV formula.
And, as also discussed, even with millions of bets, the actual result can deviate from the EV quite significantly.